SOLUTION: im trying to do x^2+9x+18 and I've tried to do 9(x+x)2+18 and (x+x)^2(9+18)

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Question 711863: im trying to do x^2+9x+18 and I've tried to do 9(x+x)2+18 and (x+x)^2(9+18)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Looking at the expression x%5E2%2B9x%2B18, we can see that the first coefficient is 1, the second coefficient is 9, and the last term is 18.


Now multiply the first coefficient 1 by the last term 18 to get %281%29%2818%29=18.


Now the question is: what two whole numbers multiply to 18 (the previous product) and add to the second coefficient 9?


To find these two numbers, we need to list all of the factors of 18 (the previous product).


Factors of 18:
1,2,3,6,9,18
-1,-2,-3,-6,-9,-18


Note: list the negative of each factor. This will allow us to find all possible combinations.


These factors pair up and multiply to 18.
1*18 = 18
2*9 = 18
3*6 = 18
(-1)*(-18) = 18
(-2)*(-9) = 18
(-3)*(-6) = 18

Now let's add up each pair of factors to see if one pair adds to the middle coefficient 9:


First NumberSecond NumberSum
1181+18=19
292+9=11
363+6=9
-1-18-1+(-18)=-19
-2-9-2+(-9)=-11
-3-6-3+(-6)=-9



From the table, we can see that the two numbers 3 and 6 add to 9 (the middle coefficient).


So the two numbers 3 and 6 both multiply to 18 and add to 9


Now replace the middle term 9x with 3x%2B6x. Remember, 3 and 6 add to 9. So this shows us that 3x%2B6x=9x.


x%5E2%2Bhighlight%283x%2B6x%29%2B18 Replace the second term 9x with 3x%2B6x.


%28x%5E2%2B3x%29%2B%286x%2B18%29 Group the terms into two pairs.


x%28x%2B3%29%2B%286x%2B18%29 Factor out the GCF x from the first group.


x%28x%2B3%29%2B6%28x%2B3%29 Factor out 6 from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.


%28x%2B6%29%28x%2B3%29 Combine like terms. Or factor out the common term x%2B3


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Answer:


So x%5E2%2B9x%2B18 factors to %28x%2B6%29%28x%2B3%29.


In other words, x%5E2%2B9x%2B18=%28x%2B6%29%28x%2B3%29.


Note: you can check the answer by expanding %28x%2B6%29%28x%2B3%29 to get x%5E2%2B9x%2B18 or by graphing the original expression and the answer (the two graphs should be identical).